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Question

lf $$2^{3}+4^{3}+6^{3}+\ldots+(2n)^{3}=kn^{2}(n+1)^{2}$$, then $$\mathrm{k}=$$


A
12
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B
1
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C
32
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D
2
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Solution

The correct option is C $$2$$
$$2^{3}+4^{3}+6^{3}+\ldots..+(2n)^{3}=2^3(1^3+2^3+3^3+\ldots.. +n^3)$$
$$=8\dfrac{n^2(n+1)^2}{4}$$
$$=2n^2(n+1)^2$$
Comparing it with $$=kn^2(n+1)^2$$, we get
$$k=2$$

Mathematics

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